Can you extrude a mesh like a 'stroke'?
Edit:

This script can apparently be used to stroke edges outward:
https://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Modeling/offset_edges

If, for some reason, you can't use the script, you can use the workaround in my old answer.

Old answer

This is just a workaround. Find an add-on if you have to do this frequently.

1 - Extrude the shape

2 - Select one face on the top and on the bottom



3 - Select linked flat faces


This should select everything on the top and bottom.

4 - Select inverse


This will select the rim edges

5 - (optional) Extrude, don't move them and Enter

6 - Shrink/fatten


You should see this result:


7 - If necessary, delete unneeded geometry

Select one face on the top - Select linked flat faces - Select inverse - Delete!